Efficient Full-Wave Characterization of Discrete High-Density Multiterminal Decoupling Capacitors for High-Speed Digital Systems

This paper presents an efficient surface-based finite-element method for the full-wave characterization of high-density and multiterminal decoupling capacitors (2, 8, 14, and any arbitrary number of terminals). In contrast to traditional finite-element methods that involve 3-D volumetric unknowns, this method reduces the unknowns one needs to solve to those on 2-D surfaces only. In addition, the reduction from the 3-D volume-based matrix to a 2-D surface-based one is achieved efficiently by exploiting the geometrical specialty of the decap structure. The entire numerical procedure is numerically rigorous without making any approximation. Its efficiency and accuracy have been demonstrated by both measurements and numerical experiments. Based on its fast and accurate solution, different design configurations of capacitors were studied to identify the optimal configuration that can maximize the performance of a decoupling capacitor. Furthermore, the full-wave model obtained from the proposed method was employed to assess the accuracy of conventional series lumped RLC capacitor models. In addition, the full-wave model was incorporated into a high-performance microprocessor's power delivery network to investigate system performance.